Impulse Trajectory and Final Controllability of Parabolic-Hyperbolic Systems

The authors analyze the existence and uniqueness of the generalized solutions to boundary-value problems for equations of parabolic-hyperbolic type with generalized functions of finite order in their right-hand sides. The motivation is the analysis of the problems of trajectory and final controllabi...

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Published inCybernetics and systems analysis Vol. 59; no. 3; pp. 417 - 427
Main Authors Semenov, V. V., Denisov, S. V.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.05.2023
Springer
Springer Nature B.V
Subjects
Artificial Intelligence
Boundary value problems
Control
Controllability
Existence theorems
Hyperbolic systems
Mathematics
Mathematics and Statistics
Norms
Processor Architectures
Software Engineering/Programming and Operating Systems
Systems Theory
Trajectory control
Uniqueness
negative norms
a priori estimates
controllability
impulse control
equations of parabolic–hyperbolic type
generalized solution
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Summary:The authors analyze the existence and uniqueness of the generalized solutions to boundary-value problems for equations of parabolic-hyperbolic type with generalized functions of finite order in their right-hand sides. The motivation is the analysis of the problems of trajectory and final controllability of systems described by these boundary-value problems and subjected to concentrated influences of impulse or point type. The systems can be considered “toy models” of the interaction of a solid body and a liquid. A priori inequalities in negative norms are obtained. The theorems of the existence and uniqueness of the generalized solutions and theorems of the trajectory and final controllability of systems with singular influences are proved.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-023-00576-0